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受欢迎的代数 >

x^3-4x^2-x+1=(x-2)^3

解答

x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}

解答

x = \frac{13 + 97}{4}, x = \frac{13 - 97}{4}

+1

十进制

x = 5.71221 \dots, x = 0.78778 \dots

求解步骤

x^{3} - 4 x^{2} - x + 1 = (x - 2)^{3}

展开

(x - 2)^{3} : x^{3} - 6 x^{2} + 12 x - 8

x^{3} - 4 x^{2} - x + 1 = x^{3} - 6 x^{2} + 12 x - 8

两边减去

x^{3} - 6 x^{2} + 12 x - 8

x^{3} - 4 x^{2} - x + 1 - (x^{3} - 6 x^{2} + 12 x - 8) = x^{3} - 6 x^{2} + 12 x - 8 - (x^{3} - 6 x^{2} + 12 x - 8)

化简

2 x^{2} - 13 x + 9 = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 13 ) \pm ( - 13 ) ^{2} - 4 \cdot 2 \cdot 9}{2 \cdot 2}

(- 13)^{2} - 4 \cdot 2 \cdot 9 = 97

x_{1, 2} = \frac{- ( - 13 ) \pm 97}{2 \cdot 2}

将解分隔开

x_{1} = \frac{- ( - 13 ) + 97}{2 \cdot 2}, x_{2} = \frac{- ( - 13 ) - 97}{2 \cdot 2}

x = \frac{- ( - 13 ) + 97}{2 \cdot 2} : \frac{13 + 97}{4}

x = \frac{- ( - 13 ) - 97}{2 \cdot 2} : \frac{13 - 97}{4}

二次方程组的解是:

x = \frac{13 + 97}{4}, x = \frac{13 - 97}{4}

作图

流行的例子

solvefor x,y^2-1=(x-1)(x-3)

so l v e f or x, y^{2} - 1 = (x - 1) (x - 3)

y^{2} + 9 y - 10 = 0

2 (x + 5) \cdot x = 300

x^2+0.9x-0.36=0

x^{2} + 0.9 x - 0.36 = 0

solvefor x,z(x+y)p+z(x-y)q=x^2+y^2

so l v e f or x, z (x + y) p + z (x - y) q = x^{2} + y^{2}